4/7 divided by 2 1/3

4/7 divided by 2 1/3

The Correct Answer and Explanation is:

To divide the fraction ( \frac{4}{7} ) by the mixed number ( 2 \frac{1}{3} ), we will follow a few simple steps.

Step 1: Convert the mixed number to an improper fraction

First, we need to convert ( 2 \frac{1}{3} ) into an improper fraction.

• To convert ( 2 \frac{1}{3} ), multiply the whole number ( 2 ) by the denominator ( 3 ), and then add the numerator ( 1 ):
  [
  2 \times 3 = 6
  ]
  [
  6 + 1 = 7
  ]
  So, ( 2 \frac{1}{3} ) is equivalent to ( \frac{7}{3} ).

Step 2: Division of fractions

Now, we need to divide ( \frac{4}{7} ) by ( \frac{7}{3} ). Dividing fractions involves multiplying the first fraction by the reciprocal (or the inverse) of the second fraction.

The reciprocal of ( \frac{7}{3} ) is ( \frac{3}{7} ).

So, the division problem becomes:
[
\frac{4}{7} \div \frac{7}{3} = \frac{4}{7} \times \frac{3}{7}
]

Step 3: Multiply the fractions

To multiply fractions, multiply the numerators (top numbers) and the denominators (bottom numbers):
[
\frac{4}{7} \times \frac{3}{7} = \frac{4 \times 3}{7 \times 7} = \frac{12}{49}
]

Step 4: Simplify the result

The fraction ( \frac{12}{49} ) is already in its simplest form because 12 and 49 do not share any common factors other than 1. Therefore, the result is ( \frac{12}{49} ).

Final Answer:

The result of ( \frac{4}{7} \div 2 \frac{1}{3} ) is ( \frac{12}{49} ).

Explanation of the steps:

1. Converting the mixed number: Mixed numbers (like ( 2 \frac{1}{3} )) need to be converted into improper fractions to make operations easier. This ensures that the division process can be carried out consistently with fractions.
2. Reciprocal multiplication: Dividing by a fraction is equivalent to multiplying by its reciprocal. This step is crucial to properly solve the division of fractions.
3. Multiplying numerators and denominators: When multiplying fractions, the numerators are multiplied together and the denominators are multiplied together to give the final result.
4. Simplification: Always simplify the resulting fraction if possible. However, in this case, ( \frac{12}{49} ) is already in its simplest form.

Thus, the correct answer is ( \frac{12}{49} ).